A bigger exchange should have the resources to account for occasional asset recoveries, and if they don't - they could charge the user for their mistakes, just not 100% 
While charging 100% sucks but charge a little amount do make sense. I imagine the recovery process for a big exchange or business is not easy. Maybe they have protocols before accessing it, have permission from this department, that department etc, I don't know how they operate but a risk of exposing the seed or private key is always there.Will it not affect transactions of ethereum and tokens on their platform if they do this?
It should not, the public key should always receive the token/coin. Maybe at that time they will disable all the withdrawal is my best guess.